# Thread: Need some help on trig identities, difference quotient, and sum-to product

1. ## Need some help on trig identities, difference quotient, and sum-to product

part 1: write one page about a place where trigonometric iddentitiesare used in real life. include the identity where it is and where it' found.

part 2: derive ane xpression for the difference quotient when the function is sin(x) and when it's cos(x). show all steps in derivation

part 3: find a real world situation where sum-to product identity is used for something other than solving calculus problems

would love any help on any part of this...gimme a link or maybe the answer in part 2's case.......thanks

2. Originally Posted by D-Rose
part 1: write one page about a place where trigonometric iddentitiesare used in real life. include the identity where it is and where it' found.

part 2: derive ane xpression for the difference quotient when the function is sin(x) and when it's cos(x). show all steps in derivation

part 3: find a real world situation where sum-to product identity is used for something other than solving calculus problems

would love any help on any part of this...gimme a link or maybe the answer in part 2's case.......thanks

This may be what you are looking for the difference quotient of the sine function:

Derivative of the Sine Function

Good luck!

3. I always wonder what is meant by "real life" in questions like this!

The "difference quotient" for function f(x) is $\displaystyle \frac{f(x+h)- f(x)}{h}$ so that would just be $\displaystyle \frac{sin(x+h)- sin(x)}{h}$ and $\displaystyle \frac{cos(x+h)- cos(x)}{h}$. It looks like that is all you need here.

For the other two questions, I would suggest you look to surveying problems.

4. Originally Posted by D-Rose
part 1: write one page about a place where trigonometric iddentitiesare used in real life. include the identity where it is and where it' found.

part 2: derive ane xpression for the difference quotient when the function is sin(x) and when it's cos(x). show all steps in derivation

part 3: find a real world situation where sum-to product identity is used for something other than solving calculus problems

would love any help on any part of this...gimme a link or maybe the answer in part 2's case.......thanks

1. Sound and Electricity are sinusoidal and anything that rotates uses trig.

2. Use the Taylor Series for sin(x) and cos(x). As x tends to 0 and is less than one it can be used.

5. Are trig identtiies related to the fourier series? They're used a lot in real life applications, so I could just list where the fourier sries is used and just say it involves use of identities....would that work??